Question

Find the largest number that will divide $1630,525$ and $1280$ leaving the remainder $6,3$ and $4$ respectively:

• A. $29$
• B. $58$
• C. $116$
• D. Can't be determined

Answer 1

The correct option is B $58$

Let us first subtract the remainders from the given numbers as follows:

$1630-6=1624$

$525-3=522$

$1280-4=1276$

Now, let us factorize $1624,522$ and $1276$ as shown below:

$1624=2\times 2\times 2\times 7\times 29522=2\times 3\times 3\times 291276=2\times 2\times 11\times 29$

We know that the largest positive integer which divides two or more integers without any remainder is called Highest Common Factor (HCF).

Therefore, the HCF of $1624,522$ and $1276$ is:

HCF$=2\times 29=58$

Hence, the largest number is $58$.